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Algorithms 2013, 6(3), 485-493; doi:10.3390/a6030485
Article

A Simple Algorithm for Solving for the Generalized Longest Common Subsequence (LCS) Problem with a Substring Exclusion Constraint

1
 and 1,2,*
Received: 14 June 2013; in revised form: 15 July 2013 / Accepted: 24 July 2013 / Published: 15 August 2013
Download PDF [164 KB, uploaded 15 August 2013]
Abstract: This paper studies the string-excluding (STR-EC)-constrained longest common subsequence (LCS) problem, a generalized LCS problem. For the two input sequences, X and Y , of lengths n andmand a constraint string, P, of length r, the goal is to find the longest common subsequence, Z, of X and Y that excludes P as a substring. The problem and its solution were first proposed by Chen and Chao, but we found that their algorithm cannot solve the problem correctly. A new dynamic programming solution for the STR-EC-LCS problem is then presented in this paper, and the correctness of the new algorithm is proven. The time complexity of the new algorithm is O(nmr).
Keywords: constrained LCS; string-excluding; dynamic programming constrained LCS; string-excluding; dynamic programming
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Zhu, D.; Wang, X. A Simple Algorithm for Solving for the Generalized Longest Common Subsequence (LCS) Problem with a Substring Exclusion Constraint. Algorithms 2013, 6, 485-493.

AMA Style

Zhu D, Wang X. A Simple Algorithm for Solving for the Generalized Longest Common Subsequence (LCS) Problem with a Substring Exclusion Constraint. Algorithms. 2013; 6(3):485-493.

Chicago/Turabian Style

Zhu, Daxin; Wang, Xiaodong. 2013. "A Simple Algorithm for Solving for the Generalized Longest Common Subsequence (LCS) Problem with a Substring Exclusion Constraint." Algorithms 6, no. 3: 485-493.


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